# Simulating Satellite Orbits and Atmospheric Drag

Delores J. Knipp
,
US Air Force Academy, Dept of Physics
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Physics students are intrigued by activities in space. To link this natural curiosity with solid problem-solving skills, we developed a spreadsheet simulation for satellites moving through an atmosphere of variable density. The simulation reviews mechanics and illustrates a method scientists might use to break a complex problem into small, solvable elements.
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## Context

Audience:

Undergraduate required course in introductory physics.

Skills and concepts that students must have mastered:

Newton's Second Law of Motion applied to circular motion
Potential and kinetic energy
Conservation of mechanical energy
Work-Energy Theorem

How the activity is situated in the course:

This is a review and knowledge-consolidation activity used three quarters of the way though the course. It is also used as a means of introducing space-related, physical effects to future aerospace officers.

National or State Education Standards addressed by this activity?:

FORMULATE AND REVISE SCIENTIFIC EXPLANATIONS AND MODELS USING LOGIC AND EVIDENCE
Motions and forces
Conservation of energy and increase in disorder

## Goals

Content/concepts goals for this activity:

Application of large scale energy conservation
Dynamic analysis
Structure of Earth's Lower Atmosphere
Iterative problem solving

Higher order thinking skills goals for this activity:

Critical data-model comparisons
Critical evaluation of competing models
Synthesis of ideas about causes and effects of motion
Synthesis of ideas about energy conservation

Other skills goals for this activity:

Working in groups
Introcution to numercal modeling

## Description of the activity/assignment

key words: energy conservation, law of atmospheres, satellite drag

The goals of this exercise are to put the laws of large-scale orbital dynamics into a space physics context while introducing numerical and semi-empirical modeling methods. The spreadsheet simulation consists of two linked spreadsheets and their associated plots. One spreadsheet contains density and temperature for the lower 1000 kilometers of the Earth's atmosphere, and the other contains the orbit simulation. A concept map guides students in developing formulations for describing satellite motion in an atmosphere whose density varies exponentially. At the conclusion of the laboratory students produce temporal profiles of altitude, velocity, energy, and drag force on a low-Earthorbiting satellite. A post-laboratory questionnaire focuses student thought on the physics and modeling process.

## Determining whether students have met the goals

Instructors review the spreadsheet results with each group of students. Students keep working on the spreadsheet until they achieve the correct solution. Students who quickly achieve the correct solution have the opportunity to do additional data-model comparisons with satellites orbits monitored by NASA, the US Air Force and the US Navy.
All students complete a post-laboratory questionnaire that focuses their thought on the physics and modeling process.